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Lecture 3

Angular Sizes,

Moon Phases, and

Ptolemy

September 12, 2018

Measuring Angles

• Apparent distances in the sky are determined by

measuring the angle between two objects.

• There are 360 degrees in a circle.

• Each degree is split into 60 arcminutes

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Angular Size

q

As distance increases, angular size decreases

q

3

Linear Size from Angular Size

180

57.3

rD

r

q

q

=

=

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The Sun and the Moon have roughly the same angular

size. However, the Sun is 400 times more distant than

the Moon. What is the linear size of the Sun compared

to that of the Moon?

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A. 400 times greater

B. 400 times smaller

C. 200 times greater

D. 200 times smaller

The Sun and the Moon have roughly the same angular

size. However, the Sun is 400 times more distant than

the Moon. What is the linear size of the Sun compared

to that of the Moon?

A. 400 times greater

B. 400 times smaller

C. 200 times greater

D. 200 times smaller

180

180

400400

Sun Sun

Sun Sun

Moon MoonMoon Moon

Moon

Moon

rD r

rD r

r

r

q

q= =

= =

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Phases of the Moon

• The Moon orbits the Earth ~ every month.

• The Moon appears to have different phases

because we see more or less of the lighted side of

the Moon depending on where it is with respect to

the Sun.

• Sidereal period: time to complete one revolution

with respect to the stars (27.3 days)

• Synodic period: time to return to same phase as

seen from Earth (29.5 days)

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Sidereal and Synodic Month8

Waning

Crescent

New Moon

Waxing

Crescent

Last Quarter

Full Moon

First Quarter

Phases of the Moon

Waxing

Gibbous

Waning

Gibbous

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Flash Applet

Animation

Phases - Photos10

Changes in the Full Moon

Laurent Laveder of Quimper, Bretagne, France photographed 12 full Moons of 2005-2006 and stitched the pictures together to make this movie.

The Moon swells and shrinks, it rocks back and forth and up and down. This is a result of the Moon's motion around its tilted, elliptical orbit. Each full Moon occurs at a different point in that orbit, and so we see it from a slightly different distance and angle. The rocking motions are called libration; because of them we can see 59% of the Moon's surface rather than the 50% you might have learned in school. Spaceweather.com 5/15/06

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When does the third quarter moon rise?

A. About 6 AM

B. About noon

C. About 6 PM

D. About midnight

When does the third quarter moon rise?

A. About 6 AM

B. About noon

C. About 6 PM

D. About midnight

E

W

first quarter

third quarter

Shape of the Earth –

Aristotle ( 384-322 BC)

• Earth’s shadow was curved during a lunar eclipse.

• Ships appeared to sink below the horizon.

• View of stars differs from different locations.

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The Geocentric Universe• Ancient people (Aristotle) “knew” from

observations that

– The stars appear fixed on the sky relative to each other.

– Planets, moon and Sun change position with respect to the stars.

– Mercury and Venus are only seen near Sun.

• These observations led them to theorize that the spherical Earth is at the center of a great celestial sphere containing all heavenly objects.

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Basic Geocentric View• Order of planets somewhat arbitrary.

• Mercury and Venus always orbit at a velocity that

keeps them near the Sun.

E

Sun

Moon

Mercury

SaturnCelestial Sphere

Jupiter

Mars

Venus

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Retrograde Motion• Direct Motion: Planets usually move from west-to-east

in the sky with respect to the stars over long periods of time.

• Retrograde Motion: Planets sometimes change direction and go east-to-west with respect to the stars

WestEast

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• All motions were on

circles (“perfect

shape”)

Ptolemy (140 AD)• Planets move on “epicycles”

• Epicycles moved on deferent that was

centered not on the Earth, but on an equant

point.

epicycle

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• Predicted positions of

planets very

accurately.

• Accepted theory for

~15 centuries!

Ptolemy (140 AD)

• Size and rates of motion on epicycles was

calculated using tabulated data

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Epicycles20

Animation(Figure 3.11 p.61)

In Ptolemy’s model, when is a planet closest to

Earth?

A. When the planet crosses

the deferent.

B. During its retrograde

westward motion.

C. When it is closest to the

equant point.

D. There is no specific time in

its orbit when the planet is

closest to Earth.